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Simplifying 3x2 + 42x + 100 = 0 Reorder the terms: 100 + 42x + 3x2 = 0 Solving 100 + 42x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 33.33333333 + 14x + x2 = 0 Move the constant term to the right: Add '-33.33333333' to each side of the equation. 33.33333333 + 14x + -33.33333333 + x2 = 0 + -33.33333333 Reorder the terms: 33.33333333 + -33.33333333 + 14x + x2 = 0 + -33.33333333 Combine like terms: 33.33333333 + -33.33333333 = 0.00000000 0.00000000 + 14x + x2 = 0 + -33.33333333 14x + x2 = 0 + -33.33333333 Combine like terms: 0 + -33.33333333 = -33.33333333 14x + x2 = -33.33333333 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -33.33333333 + 49 Reorder the terms: 49 + 14x + x2 = -33.33333333 + 49 Combine like terms: -33.33333333 + 49 = 15.66666667 49 + 14x + x2 = 15.66666667 Factor a perfect square on the left side: (x + 7)(x + 7) = 15.66666667 Calculate the square root of the right side: 3.958114029 Break this problem into two subproblems by setting (x + 7) equal to 3.958114029 and -3.958114029.Subproblem 1
x + 7 = 3.958114029 Simplifying x + 7 = 3.958114029 Reorder the terms: 7 + x = 3.958114029 Solving 7 + x = 3.958114029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.958114029 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.958114029 + -7 x = 3.958114029 + -7 Combine like terms: 3.958114029 + -7 = -3.041885971 x = -3.041885971 Simplifying x = -3.041885971Subproblem 2
x + 7 = -3.958114029 Simplifying x + 7 = -3.958114029 Reorder the terms: 7 + x = -3.958114029 Solving 7 + x = -3.958114029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.958114029 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.958114029 + -7 x = -3.958114029 + -7 Combine like terms: -3.958114029 + -7 = -10.958114029 x = -10.958114029 Simplifying x = -10.958114029Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.041885971, -10.958114029}
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